Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Momentum Crashes
Kent Daniel & Tobias Moskowitz†
† Columbia
Business School & Chicago-Booth
The Q -G ROUP : FALL S EMINAR
17 October 2012
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Introduction
Momentum
This paper does a “deep-dive” into one particular
factor/anomaly: price momentum.
It is employed by many (most?) quantitative managers.
Grinblatt and Titman (1989, 1993), Carhart (1997), and
subsequent work argue that mutual funds also employ
momentum.
Historically, momentum strategies deliver high premia.
Over the post WWII period, through 2008, the long-short
equity momentum strategy we’ll examine had an average
return of 16.5%/year, a market beta of -0.125, and an
annualized Sharpe-ratio of 0.82.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Introduction
Evidence of Momentum
Momentum is pervasive:
US Equities: Jegadeesh and Titman (1993, 2001).
Developed Equities: Rouwenhorst (1998)
Emerging Equities: Rouwenhorst (1999)
Industries & Firm Specific (Equity): Moskowitz and
Grinblatt (1999), Grundy and Martin (2001).
Country Equity Indices: Asness, Liew, and Stevens (1997)
Currencies: Okunev and White (2003)
Commodities: Erb and Harvey (2006)
Futures: Asness, Moskowitz, and Pedersen (2008),
Moskowitz, Ooi, and Pedersen (2012).
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Introduction
Momentum
However, momentum strategy returns exhibit significant
negative skewness:
e.g., in March-May 2009, equity momentum strategies
suffered severe losses.
The April 2009 return was the worst since August, 1932.
Monthly momentum return skewness is -6.3.
For comparison, HML is +1.8, and the market is -0.58
The maximum monthly momentum return in our sample is
26.1%.
The 5 worst are -79%, -60%, -46%, -44%, and -42%.
Much like “carry-trade” strategies in currencies, momentum
strategies are sometimes perceived like selling out-of-the
money put options (see, e.g., Brunnermeier, Nagel, and
Pedersen (2008))
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Literature Review
Behavioral theories of momentum:
Barberis, Shleifer, and Vishny (1998) Daniel, Hirshleifer,
and Subrahmanyam (1998), Hong and Stein (1999),
George and Hwang (2004), Grinblatt and Han (2005)
Time dependence in momentum risk:
Grundy and Martin (2001) show that the market beta of
momentum strategies is highly dependent on the lagged
market return.
They further argue that a momentum portfolio which
hedges out market & size risk exhibits consistently good
performance. (using ex-post β̂s).
Time dependence in momentum returns:
Cooper, Gutierrez, and Hameed (2004) demonstrate the
state dependence of momentum strategy returns
They don’t control for conditional variations in risk.
“Optionality” in momentum returns:
Rouwenhorst (1998), Chan (1988), DeBondt and Thaler
(1987).
Q -Group Fall Seminar – 17·October·2012
Daniel & Moskowitz, Momentum Crashes
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Momentum: Portfolio Construction
At the end of each month, we form 10 value-weighted
momenutum portfolios on the basis of prior (12,2) return:
Over the one-month holding period, we will evaluate the
return of the top and bottom (“winner” and “loser”) deciles.
We also consider the long-short portfolio that invests $1 in
the winner portfolio, and shorts $1 worth of the loser
portfolio (=WML)
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Momentum: Portfolio Construction
At the end of each month, we re-form the portfolios based on
the updated ranking-period return:
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Momentum: Portfolio Construction
While the portfolio are reblanced at the end of each month,
we generate daily returns for each of the ten portfolios.
This is necessary to accurately estimate the conditional risk
of the portfolios.
For a firm to be included in the portfolio, we require that:
The firm remain be listed on the NYSE, AMEX or NASDAQ.
The shares be common shares only (share-code 10 or 11)
The firm have valid prices and share data during the
formation period (for value weighting).
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Long-Only Investment Strategy Returns
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Long-Only Investment Strategy Returns
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Long-Only Investment Strategy Returns
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Long-Only Investment Strategy Returns
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
2009-10 Momentum Performance
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Momentum in the Great Depression
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Cumulative Momentum Returns
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Momentum Portfolio Characteristics: 1927-2010
µ
σ
α
t(α)
β
SR
sk(m)
sk(d)
1
0.2
34.4
-11.2
(-5.8)
1.56
0.01
0.13
-0.21
2
4.7
28.7
-5.1
(-3.5)
1.34
0.17
-0.05
0.16
3
4.9
24.7
-3.7
(-3.2)
1.18
0.20
-0.12
0.15
Momentum Decile Portfolios
4
5
6
7
6.6
6.7
7.5
8.4
22.6
21.0
20.4
19.5
-1.4
-0.9
-0.0
1.3
(-1.5)
(-1.1)
(-0.1)
(1.9)
1.10
1.03
1.03
0.97
0.29
0.32
0.37
0.43
0.17
-0.05
-0.32
-0.65
0.37
-0.10
0.02
-0.49
8
9.9
18.8
3.1
(4.4)
0.93
0.53
-0.53
-0.58
9
10.8
19.8
3.7
(4.4)
0.96
0.54
-0.81
-0.72
10
14.6
22.7
7.2
(5.4)
1.01
0.64
-0.92
-0.74
wml
14.4
27.7
18.4
(6.5)
-0.54
0.52
-6.32
-1.47
Mkt
7.4
18.9
0
(0)
1
0.39
-0.58
-0.44
Note that the skewness is less pronounced for the daily returns than for
the monthly.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
10 Worst Monthly Momentum Returns
R ANK
1
2
3
4
5
6
7
8
9
10
11
M ONTH
1932-08
1932-07
2009-04
1939-09
1933-04
2001-01
2009-03
1938-06
1931-06
1933-05
2009-08
M OMt
-0.7896
-0.6011
-0.4599
-0.4394
-0.4233
-0.4218
-0.3962
-0.3314
-0.3009
-0.2839
-0.2484
M KT-2 Y
-0.6767
-0.7487
-0.4136
-0.2140
-0.5904
0.1139
-0.4539
-0.2744
-0.4775
-0.3714
-0.2719
M KTt
0.3660
0.3375
0.1106
0.1596
0.3837
0.0395
0.0877
0.2361
0.1380
0.2119
0.0319
M KT-2 Y is the lagged 2-year market return
M KTt is the contemporaneous (1-month) market return.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Literature Review
Portfolio Construction
Crash Characterization
Bear Market Momentum Performance
The preceding table shows that the momentum strategy
suffers its worst performance at “turning points,” following
large market declines:
In June 1932, the market “bottomed.”
in July-August 1932, the market rose by 82%.
Over these 2 months, losers outperform winners by 206%.
losers gain 236%, winners gain 30%.
On March 9, 2009 the US equity market bottomed.
In March-May 2009, the market was up by 29%.
losers outperform winners by 149%.
losers gain 156%, winners gain 6.5%.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Momentum Beta
As of March 2009, many the firms in the Loser portfolio
had fallen by 90% or more.
These were firms like Citigroup, Bank of America, Ford,
GM, and International Paper (which was levered)
In contrast, the Winner portfolio was composed of
defensive or counter-cyclical firms like Autozone.
The loser firms, in particular, were often extremely levered,
and at risk of bankruptcy.
Their common stock was effectively an out-of-the-money
option on the firm value (à là (Merton 1974))
This suggests that there were potentially large differences
in the market betas of the winner and loser portfolios
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Market Beta and Momentum - 1931-1945
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Market Beta and Momentum - 1999-2010
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Hedging market risk
Consistent with Grundy and Martin (2001), this evidence
suggests hedging out market risk could be beneficial.
We estimate rolling 42-day (2-month) betas
We regress rWML,t on contemporaneous Market, and 10
lags of the market return.
This is particularly important in the early period, and for the
low momentum portfolios, because of non-trading/illiquidity
biases.
We then construct a hedged WML portfolio:
h
e
r̃WML,t
= r̃WML,t − βt · r̃m,t
,
where βt is the forward-looking rolling-beta estimate.
This closely follows the procedure of Grundy and Martin
(2001).
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Hedged Momentum Portfolio Performance
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Grundy and Martin (2001) perform their analysis using
ex-post betas becuase:
The dynamics of beta are complicated.
They had only monthly data.
Also, as long as the realized beta is uncorrelatted with the
contemporaneous market return, there procedure should
introduce a bias in the efficacy of the hedge ...
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Estimating Beta
There is a strong Up- and Down-β differential in bear markets:
�
� e
R̃WML,t = [α0 + αB IB ] + β0 + βB IB + βB,U (IB · ĨU ) R̃m,t
+ �˜t
Coeff.
α̂0
Variable
1
α̂B
IB
β̂0
e
R̃m,t
β̂B
e
IB · R̃m,t
β̂B,U
2
Radj
e
IB · ĨU · R̃m,t
Estimated Coefficients
(t-statistics in parentheses)
(1)
(2)
(3)
(4)
0.017
0.016
0.016
0.022
(7.1)
(6.8)
(6.9)
(7.5)
-0.019
0.007
(-3.4)
(0.9)
-0.543
0.038
0.054
0.054
(-12.6)
(0.7)
(0.7)
(0.7)
-1.198
-0.736
-0.788
(-15.5)
(-6.1)
(-7.4)
-0.794
-0.695
(-5.0)
(-6.0)
0.136
0.321
0.339
0.339
IB = 1 when the past 2-year market return is non-positive – there are 177 Bear-market months.
ĨU = 1 when Rm,t > 0. This is not an ex-ante variable.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Where is the Option?
This optionality is mostly in the loser portfolio:
For the past-loser portfolio, β̂B,U = 0.60.
For the past-winner portfolio, β̂B,U = −0.21.
The optionality is not present in BulL markets:
For past-loser portfolio, β̂L,U = 0.02.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
WML “Option”
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
The regression results show that the up-beta of the WML
portfolio is much more negative than the down-beta.
This means, if you use a forward looking beta estimate:
You hedge more (i.e., buy more market) when then market
is going to rise.
This imparts a large positve bias to the estimate of the
hedged portfolio returns.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Hedged Momentum Portfolio Performance
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Forecasting Crashes
We have seen that the payoff associated with the WML
portfolio has short-option-like characteristics.
It seems likely this this option will be more costly when
market variance is higher
This is also consistent with behavioral motivations for the
premium
Based on this we investigate whether other variables
associated with perceived risk affect the payoff to
momentum strategies.
Specifically we look at a realized volatility – related to the
VIX.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
Market Beta
Performance of Hedged Portfolios
WML “Option”
Forecasting Crashes
Forecasting Momentum Returns
2
2
r̃WML,t = γ0 + γB · IB,t−1 + γσm2 · σ̂m,t−1
+ γint · IB,t−1 · σ̂m,t−1
+ �˜t
1
2
3
4
5
γ0
0.0006
(5.59)
0.0008
(6.78)
0.0009
(6.98)
0.0006
(6.06)
0.0006
(4.87)
γB
-0.0012
(-4.51)
-0.0006
(-2.04)
-0.0004
(0.36)
Daniel & Moskowitz, Momentum Crashes
γσm2
γint
-3.69
(-6.07)
-3.07
(-4.54)
-0.54
(-0.53)
-4.75
(-7.17)
-4.50
(-3.30)
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
Momentum in Other Markets
We now investigate whether the predictability and
optionality patterns are also present in other markets
We examine 3 other equity markets, and 4 other asset
classes.
Data is similar to that in Asness, Moskowitz, and Pedersen
(2008).
Our momentum measure is 12-2 in each market
momentum portfolio is long top third, short bottom third.
We use a market return that corresponds to the asset
universe in which the momentum strategy is constructed.
VW for equities, EW for other asset classes.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
Data
International Equities
US, UK, Continental Europe, and Japan
In each market, universe is largest market capitalization
firms, such that we include 90% of the total market cap.
comprises 15-20% of names in each market.
Other Asset Classes
Commodities
27 commodities from 8 exchanges.
Oil and Gas, Metals, Agricultural.
Currencies
9 Currencies.
Australia, Canada, Germany (spliced with the Euro), Japan,
New Zealand, Norway, Sweden, Switzerland, and U.K.
Bonds
10 Government Bonds.
Australia, Canada, Denmark, Germany, Japan, Norway,
Sweden, Switzerland, U.K., and U.S.
Equities
18 Equity
Indices
Daniel & Moskowitz,
Momentum
Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
International Equity Market Momentum
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
Past Market Returns and Market Variance
2
2
e
R̃tmom = [α0 + αB IB + αV σ̂m
] + [β0 + βB IB + βV σ̂m
]R̃m,t
+ �˜t .
α̂0
α̂B
α̂V
β̂0
β̂B
β̂V
Europe
0.010
(4.2)
0.003
(0.5)
-0.143
(-2.7)
0.109
(2.4)
-0.372
(-4.3)
-1.787
(-3.0)
Japan
0.005
(1.4)
0.002
(0.4)
-0.150
(-2.3)
0.242
(4.4)
-0.539
(-6.8)
0.449
(0.5)
Daniel & Moskowitz, Momentum Crashes
UK
0.009
(3.5)
-0.001
(-0.1)
-0.141
(-2.3)
0.069
(1.6)
-0.092
(-1.2)
-2.390
(-2.9)
US
0.008
(3.2)
0.007
(1.2)
-0.197
(-3.3)
0.216
(3.6)
-0.523
(-5.0)
-1.836
(-2.1)
Q -Group Fall Seminar
global
0.007
(4.7)
0.002
(0.4)
-0.116
(-3.1)
0.052
(1.4)
-0.201
(-2.8)
-1.011
(-1.9)
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
Optionality in Bear Markets
�
� e
R̃tmom = [α0 + αB IB ] + β0 + βB IB + βB,U (IB · ĨU ) R̃m,t
+ �˜t
α̂0
α̂B
β̂0
β̂B
β̂B,U
Europe
0.007
(3.0)
0.012
(1.8)
0.075
(1.7)
-0.305
(-2.6)
-0.443
(-2.5)
Japan
-0.001
(-0.3)
0.013
(1.8)
0.248
(4.7)
-0.284
(-2.0)
-0.392
(-2.1)
Daniel & Moskowitz, Momentum Crashes
UK
0.006
(2.6)
0.004
(0.6)
0.026
(0.6)
0.016
(0.1)
-0.329
(-2.2)
US
0.003
(1.2)
0.005
(0.5)
0.167
(2.9)
-0.556
(-3.2)
-0.085
(-0.3)
Q -Group Fall Seminar
global
0.005
(3.2)
0.005
(1.0)
0.029
(0.8)
-0.092
(-0.9)
-0.338
(-2.2)
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
Other Asset Class Momentum
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
Past Market Returns and Market Variance
2
2
e
R̃tmom = [α0 + αB IB + αV σ̂m
] + [β0 + βB IB + βV σ̂m
]R̃m,t
+ �˜t
α̂0
α̂B
α̂V
β̂0
β̂B
β̂V
Bonds
0.001
(1.2)
-0.000
(-0.0)
-0.029
(-1.4)
0.290
(3.7)
-0.448
(-2.9)
-1.145
(-0.8)
Commod’s
0.013
(3.2)
-0.007
(-1.0)
-0.059
(-0.7)
0.250
(2.7)
-0.718
(-4.1)
0.876
(0.5)
Currencies
0.006
(2.8)
-0.009
(-3.0)
-0.013
(-0.4)
0.267
(2.9)
-0.987
(-7.3)
0.173
(0.2)
Daniel & Moskowitz, Momentum Crashes
Equities
0.008
(3.8)
-0.001
(-0.2)
-0.020
(-0.5)
0.300
(6.2)
-0.585
(-7.0)
-0.957
(-1.4)
all
0.004
(4.4)
-0.001
(-0.4)
-0.025
(-1.2)
0.188
(2.7)
-0.360
(-2.6)
-1.558
(-1.5)
Q -Group Fall Seminar
all+stock
0.005
(5.5)
0.000
(0.0)
-0.049
(-2.3)
0.109
(2.3)
-0.238
(-2.4)
-1.363
(-1.9)
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
Optionality in Bear Markets
�
� e
R̃tmom = [α0 + αB IB ] + β0 + βB IB + βB,U (IB · ĨU ) R̃m,t
+ �˜t
α̂0
α̂B
β̂0
β̂B
β̂B,U
Bonds
-0.002
(-1.5)
0.005
(1.5)
0.287
(4.5)
-0.346
(-0.9)
-0.211
(-0.4)
Commod’s
0.009
(2.4)
0.017
(1.8)
0.288
(3.7)
0.040
(0.1)
-1.327
(-2.6)
Currencies
0.003
(1.7)
0.008
(2.0)
0.302
(3.4)
-0.498
(-1.8)
-0.889
(-2.4)
Daniel & Moskowitz, Momentum Crashes
Equities
0.005
(2.4)
0.010
(2.1)
0.283
(6.1)
-0.474
(-4.2)
-0.338
(-1.9)
Q -Group Fall Seminar
all
0.002
(2.3)
0.008
(2.7)
0.183
(2.8)
0.260
(0.8)
-1.138
(-2.7)
all+stock
0.003
(3.4)
0.007
(2.3)
0.094
(2.1)
-0.024
(-0.2)
-0.692
(-3.2)
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
Conclusions & Future Work
1
2
In “normal” environments, the market appears to
underreact to public information, resulting in consistent
price momentum.
However, in extreme market enviroments, the market
prices of severe past losers embody a very high premium.
When market conditions ameliorate, these losers
experience strong gains, resulting in a momentum crash.
The expected gains from the loser portfolio are related to
both past market losses, and lagged market volatility.
3
Market risk of momentum portfolios varies dramatically, but
does not appear to explain the variation in the premia
earned by momentum.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
Possible Behavioral Explanations
Recent behavioral work suggests that when an event has
strong affective content, the price that individuals are
willing to pay to avoid bad outcomes is not closely related
to the probabilities of the event.
Rottenstreich and Hsee (2001) attempts to explore
people’s willingness to pay to avoid bad outcomes
One outcome – an electric shock – was described as short,
painful, but not dangerous.
In contrast, a second control group, was told that there was
a chance that they could lose $20 of their payment.
Probabilties were either stated to be 1% or 99%.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
Rottenstreich and Hsee (2001)
Subjects were willing to pay $1 to avoid a 1% chance, and
$18 to avoid a 99% chance of losing the $20.
For the electric shock, in contrast, the difference in
probability made little difference to median willingness to
pay: $7 to avoid a 1% chance, and $10 to avoid a 99%
chance.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
References I
Asness, Clifford S., John M. Liew, and Ross L. Stevens, 1997, Parallels between the cross-sectional predictability of
stock and country returns, Journal of Portfolio Management 23, 79–87.
Asness, Clifford S., Toby Moskowitz, and Lasse Pedersen, 2008, Value and momentum everywhere, University of
Chicago working paper.
Barberis, Nicholas, Andrei Shleifer, and Robert Vishny, 1998, A model of investor sentiment, Journal of Financial
Economics 49, 307–343.
Brunnermeier, Markus K., Stefan Nagel, and Lasse H. Pedersen, 2008, Carry trades and currency crashes, NBER
Macroeconomics Annual.
Carhart, Mark M., 1997, On persistence in mutual fund performance, Journal of Finance 52, 57–82.
Chan, K.C., 1988, On the contrarian investment strategy, Journal of Business 61, 147–163.
Cooper, Michael J., Roberto C. Gutierrez, and Allaudeen Hameed, 2004, Market states and momentum, Journal of
Finance 59, 1345–1365.
Daniel, Kent D., David Hirshleifer, and Avanidhar Subrahmanyam, 1998, Investor psychology and security market
under- and over-reactions, Journal of Finance 53, 1839–1886.
DeBondt, Werner F. M., and Richard H. Thaler, 1987, Further evidence on investor overreaction and stock market
seasonality, Journal of Finance 42, 557–581.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
References II
Erb, Claude B., and Campbell R. Harvey, 2006, The strategic and tactical value of commodity futures, Financial
Analysts Journal 62, 69–97.
George, Thomas J., and Chuan-Yang Hwang, 2004, The 52-week high and momentum investing, The Journal of
Finance 59, 2145–2176.
Grinblatt, Mark, and Bing Han, 2005, Prospect theory, mental accounting and momentum, Journal of Financial
Economics 78, 311–339.
Grundy, Bruce, and J. Spencer Martin, 2001, Understanding the nature of the risks and the source of the rewards to
momentum investing, Review of Financial Studies 14, 29–78.
Hong, Harrison, and Jeremy C. Stein, 1999, A unified theory of underreaction, momentum trading and overreaction
in asset markets, Journal of Finance 54, 2143–2184.
Jegadeesh, Narasimhan, and Sheridan Titman, 1993, Returns to buying winners and selling losers: Implications for
stock market efficiency, Journal of Finance 48, 65–91.
, 2001, Profitability of momentum strategies: An evaluation of alternative explanations, Journal of Finance
56, 699–720.
Merton, Robert C., 1974, On the pricing of corporate debt: The risk structure of interest rates, The Journal of
Finance 29, 449–470.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012
Momentum in Investment Strategies
Momemtum Basics
US Equity Momentum: Risk & Return
International Equities/Other Asset Classes
International Equity Markets
Other Asset Class Momentum
References III
Moskowitz, Tobias J., and Mark Grinblatt, 1999, Do industries explain momentum?, The Journal of Finance 54,
1249–1290.
Moskowitz, Tobias J., Yoa Hua Ooi, and Lasse H. Pedersen, 2012, Time series momentum, Journal of Financial
Economics 104, 228–250 University of Chicago Working Paper.
Okunev, John, and Derek White, 2003, Do momentum-based strategies still work in foreign currency markets?,
Journal of Financial and Quantitative Analysis 38, 425–447.
Rottenstreich, Yuval, and Chris K. Hsee, 2001, Money, kisses, and electric shocks: On the affective psychology of
risk, Psychological Science 12, 185–190.
Rouwenhorst, K. Geert, 1998, International momentum strategies, Journal of Finance 53, 267–284.
, 1999, Local return factors and turnover in emerging stock markets, Journal of Finance 54, 1439–1464.
Daniel & Moskowitz, Momentum Crashes
Q -Group Fall Seminar
– 17·October·2012